In order for you to start any type of meaningful disccusions with potential investors, you need a business plan. You mention that you can't answer the question as to when the business might be profitable or what the potential profits might be. "Being sure" that your business will be profitable won't satisfy many investors. Right now, that is just your opinion. You need to back up your conviction with facts and information. You need to put together financial projections. That will help you answer your question of how much to ask for, but more important, to give investors an idea as to what their initial investment might be worth a few years down the road.
One other thing that works against you, is that you say that you cannot add any money to the $20,000. Unless you are raising money from friends and/or family, it will be nearly impossible to get someone to invest money if you are not willing to put "skin in the game." If you run out of money developing this business, what is to stop you from walking away?
The last thing that you need is to be able to show potential investors proof of concept, a working model if you will. Most investors are not going to fund ideas.
Ed Baloga, CPA / MBA Principal CFO Baloga Associates ebaloga@baloga-associates.comwww.twitter.com/edbaloga

Using the numbers that you show above, you are correct in that your net profit margin is $30 per unit. The $500 for rent that you mention is a fixed overhead item. It isn't related to the number of pieces you sell each month. Yes, if of a sudden you start selling thousands of pieces per month, you will need additional warehousing, but for your purposes, it is fixed overhead. The $500 per month probably doesn't change whether you sell 1 piece or 50.
The $500 comes into the calculation of how many pieces you need to sell each month to break even, i.e., 17 units. You now need to ask yourself this, are you selling more or less than 17 pieces each month? If your volume is less than 17, can you raise your selling price (without sacrificing additional sales) to make up the difference?
The questions are no different than what larger companies face. If you decide that you can’t raise your prices, you need to take your best guess as to how long it will be to increase your unit volume. Related to this is how much cash do you have to fund your losses?
Ed Baloga, CPA / MBA Principal CFO Baloga Associates ebaloga@baloga-associates.comwww.twitter.com/edbaloga

Abigail,
I would suggest that you visit the SBA web site - www.sba.gov. They do a good job of explaining the elements of a busimess plan.
Ed Baloga, CPA / MBA Principal CFO Baloga Associates ebaloga@baloga-associates.comwww.twitter.com/edbaloga

In general, the more detail that you can supply the better. It is not necessary to have all of the detail in the main part of the plan; it can be in separate exhibits. The key are the assumptions that you use to generate your figures. If you are coming up with projections off the top of your head, then that might not inspire a great deal of confidence in the reader. Are your assumptions are supported by data driven facts? For example, if your plan is for a bricks and mortar retail store, an important piece of information is the amount of traffic that drives by the store. This type of data is probably available from your state’s transportation department.
Are you able to gather benchmarking statistics from an industry association? Again, using the retail store as an example, if you indicate that the store will generate $10 per sq. ft. in revenue each month, but the industry statistics show that the average is closer to $6 per sq. ft., you need to demonstrate why your $10 figure is reasonable.
I hope this gives you an idea or two. If you would like to discuss with me in greater detail, don’t hesitate to contact me.
Ed Baloga, CPA / MBA Principal CFO Baloga Associates ebaloga@baloga-associates.comwww.twitter.com/edbaloga

You should not be dissolving the LLC as you go along. Dissolving the LLC means that the entity ceases to exist. No need to go through all of that expense and aggravation.
Just register as a foreign entity with the state that you are living in. Depending upon the state, you may have to "un-register" as a foreign entity when you leave the state.
Feel free to contact me directly if you would like to discuss this "off-line."